The proposal (REF ) also has another problem, related to dualities. For all the domain walls studied (\(Sp(N)\)  with \(F\le N+2\)  and \(SU(N)\)  with \(F \le N+1\) ), there is always a non trivial duality incarnating the equivalence between a \(k\) -wall and the \(h-k\)  parity reversed wall. Here, however there is not a \(\mathcal {N}=2\)  duality from which one can hope to derive such an \(\mathcal {N}=1\)  duality. Indeed, the \(\mathcal {N}=2\)  duality satisfied by the \(\mathcal {N}=2\)  cousin of (REF ) is [1]}
\(\begin{array}{c} U(k)^{\mathcal {N}=2}_{\frac{N-1}{2}} \,\,\,\,\, \text{w/ $(N+1,0)$ flavors} \\ \mathcal {W}_{\mathcal {N}=2}=0 \end{array}\Longleftrightarrow \begin{array}{c} U(N+1-k)^{\mathcal {N}=2}_{-\frac{N-1}{2}} \,\,\,\,\, \text{w/ $(0,N+1)$ flavors} \\ \mathcal {W}_{\mathcal {N}=2}=\mu \, {\mathfrak {M}}\end{array}\) 
